Being that the heater core is sometimes the highest point in the cooling system, it's possible to get an air bubble in there. Air in the system will keep you from getting heat.
Your description sounds like there's air in the system. Cool then hot, then cooling..
Try splicing a prestone flush/fill T into one of the two heater hoses and ensure the system is topped off that way. Some of the local guys showed me this as a trick and at first I thought it was odd. Yet when you have odd behavior from the cooling system, it starts to make a lot more sense.
